Despite a groundswell of demand from customers to improve factory conditions overseas, most American retailers have bowed out of an international fire and building safety agreement to reform the garment industry in Bangladesh.

The deadline to join the Accord on Fire and Building Safety, which legally requires companies to perform independent inspections of their supplier factories in Bangladesh and pay for necessary safety improvements, came and went Wednesday with few U.S. retailers signing on. Of the 31 garment and retail brands sourcing from Bangladesh that joined, only two from the U.S. have added their names — PVH, the parent company of Calvin Klein and Tommy Hilfiger, and Abercrombie & Fitch.

The absence of major U.S. clothing companies such as Gap in the effort marks a sharp disconnect from those consumers who say they want more ethically made clothes in the retail marketplace. Online petitions collected more than a million signatures calling for Gap, which includes Old Navy and Banana Republic, to sign the accord in the wake of a factory collapse in Bangladesh that killed more than 1,100 workers.

Resistance from Gap and Wal-Mart probably deterred other retailers from getting on board, experts say. And sharp criticism from the Washington, D.C.-based National Retail Federation, which Wednesday lambasted the accord for serving union interests, is likely to discourage many more American retailers from joining. That could undermine the overall effect of the accord — about 80 percent of the Bangladeshi garment exports go to Europe and the U.S.

“If this is a collective effort, with many of the major brands and retailers working together, then the effects will be more broad-based,” said Eli Friedman, assistant professor at Cornell University’s Department of International and Comparative Labor and an expert in labor relations in Asia.

San Francisco-based Gap said Tuesday it was “six sentences away” from signing, but wanted to change the accord so retailers have more protection from the potential risk of lawsuits. But they failed to strike an agreement with labor groups by the Wednesday deadline. Wal-Mart, meanwhile, has rejected the accord in favor of a self-regulated safety program in Bangladesh and has begun checking the 279 factories that supply its stores.

Consumers, who for weeks have taken to the streets and social media to pressure clothing companies to sign the safety accord, on Wednesday slammed Gap on Facebook for spitting “on freshly dug graves of 1,100 innocent, honest, hardworking people” and promoting a “fashion of blood brand.” Dozens of customers pledged to stop shopping at the chain and wrote they had cut up their Gap credit cards.

Experts say American retailers can expect that backlash to continue: “If Gap does not sign on, Gap will be the target and the brand that (activists) go after,” said Dara O’Rourke, a professor at UC Berkeley and expert in global manufacturing and consumer issues.

The demand for more transparency in supply chains has grown in recent years with each allegation of poor working conditions at Apple’s (AAPL) Foxconn supplier in China or at a Nike factory, said John Paluszek, senior counsel at marketing agency Ketchum and an expert in corporate social responsibility. The April 24 garment factory collapse in Bangladesh was a tipping point for many consumers.

“Over the years, frankly, it’s been building in fits and starts,” Paluszek said.

Since the Bangladesh factory disaster, many consumers are for the first time thinking about where their clothes come from and who makes them.

“Immediately after, I was really trying to think if I had any clothes made in Bangladesh,” Lafayette resident Alex Dadiomov said while shopping Wednesday afternoon in downtown Walnut Creek.

Consumers are more committed to ending abuses in the supply chain and want their favorite stores to be, too, Paluszek said. If stores aren’t transparent, some shoppers will go elsewhere — perhaps to the European brands that signed the accord.

“There is an overall reputational risk here,” Paluszek said.

Alexandra Khryashcheva of San Ramon said she was so disturbed by the news of the Rana Plaza disaster that she started buying American-made clothes, something she “didn’t think about doing” before. On Wednesday, she said she had just picked up her first pair of jeans with the “made in the U.S.A.” label.

But, she admitted, changing habits can take time. She had also stopped in the Gap in downtown Walnut Creek during her lunch break.

But, she said: “I’m starting this change.”

Contact Heather Somerville at 925-977-8418. Follow her at Twitter.com/heathersomervil.